SOLUTION: Please help me solve this word problem An equilateral triangle is plotted on a coordinate plane with two vertices at (0,0) and (10,0). What would the coordinates be before the thi

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Question 867354: Please help me solve this word problem An equilateral triangle is plotted on a coordinate plane with two vertices at (0,0) and (10,0). What would the coordinates be before the third vertex?
Found 2 solutions by richard1234, mananth:
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Either (5, 5 sqrt(3)) or (5, -5 sqrt(3)). Not enough info to determine which point.

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
let the third vertex be A
A(x,y), B(0,0) C(10,0)
distance AB=BC=CA =10( equlateral triangle)
distance formula
d=+sqrt+%28%28x1-x2%29%5E2%2B%28y1-y2%29%5E2%29
d%5E2=%28%28x1-x2%29%5E2%2B%28y1-y2%29%5E2%29
AB = x^2-y^2
AC=(x-10)^2+y2
AB=AC
x^2-y^2=(x-10)^2+y2
x^2+y^2=(x^2-20x+100+y2)
20x=100
x=5
Plug x
x^2+y^2=100
25+y^2=100
y^2=75
y=+/-5sqrt(3)
A (x,5sqrt(3)) , (5,-5sqrt(3))